On ferroelectric phase transitions: Change-over from the mean-field-like to the true critical behavior

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Abstract
The transition from the mean-field-like to the true critical behavior for uniaxial ferroelectrics is studied by a parquet graph expansion. Both the cases of finite and vanishingly small dipolar interaction are considered as special cases of a d = 4 - ε-dimensional isotropic model. As a main result we obtain an equation of state which is valid in the whole temperature region to a well-defined degree of accuracy. The connection with renormalization-group ideas and the self-consistent phonon approximation is stated and the critical exponents are in agreement to order ε with those obtained by the ε-expansion. The renormalized electrostrictive coupling constant is also discussed.